How many times is the following loop executed? As in, how many times will the control reach loop body?for(int i = 10; i

Question

How many times is the following loop executed? As in, how many times will the control reach loop body?for(int i = 10; i < 20; i+=2) {  //loop body}

BlackTom AI · Accepted Answer

The loop variable i takes the values 10, 12, 14, 16, 18 while the condition i < 20 holds, so the body executes five times.

1. Relevant knowledge points and concepts
- A for loop for(int i = start; i < limit; i += step) initializes i to start, checks the condition (i < limit) before each iteration, executes the body only when the condition is true, then applies i += step after each body execution.
- The loop runs for every value of i in the arithmetic sequence start, start+step, start+2·step, ... as long as each value satisfies the condition.

2. Step-by-step reasoning
- Initialization: i = 10.
- Condition check: 10 < 20? Yes → execute body (1st time).
- Increment: i = 10 + 2 = 12.
- Condition check: 12 < 20? Yes → execute body (2nd time).
- Increment: i = 12 + 2 = 14.
- Condition check: 14 < 20? Yes → execute body (3rd time).
- Increment: i = 14 + 2 = 16.
- Condition check: 16 < 20? Yes → execute body (4th time).
- Increment: i = 16 + 2 = 18.
- Condition check: 18 < 20? Yes → execute body (5th time).
- Increment: i = 18 + 2 = 20.
- Condition check: 20 < 20? No → loop stops.

3. Intermediate calculations
- Sequence of i values that enter the body: 10, 12, 14, 16, 18.
- Count = ((last_value - start)/step) + 1 = ((18 - 10)/2) + 1 = (8/2) + 1 = 4 + 1 = 5.
- General formula when using i < limit: count = floor((limit - 1 - start)/step) + 1.

4. Why the correct answer is correct
- The loop condition is strict less-than (< 20), so 20 is not included. The step is 2, so starting at 10 the last valid value below 20 is 18, giving five iterations as shown.

5. Why other possible answers would be incorrect
- If someone answers 6, they likely (incorrectly) included 20. If they answer 4, they may have miscounted the sequence or stopped at 16. An answer like 0 or infinite would ignore the condition and increment behavior.

6. Conclusion
- The loop body is reached 5 times, which matches the provided answer: 5.

How many times is the following loop executed? As in, how many times will the control reach loop body?for(int i = 10; i < 20; i+=2) { //loop body}Numerical

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